Properties

Label 11760bq
Number of curves 8
Conductor 11760
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("11760.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11760bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.p7 11760bq1 [0, -1, 0, -16, 4096] [2] 6144 \(\Gamma_0(N)\)-optimal
11760.p6 11760bq2 [0, -1, 0, -3936, 95040] [2, 2] 12288  
11760.p5 11760bq3 [0, -1, 0, -7856, -121344] [2, 2] 24576  
11760.p4 11760bq4 [0, -1, 0, -62736, 6069120] [2] 24576  
11760.p2 11760bq5 [0, -1, 0, -105856, -13214144] [2, 2] 49152  
11760.p8 11760bq6 [0, -1, 0, 27424, -939840] [2] 49152  
11760.p1 11760bq7 [0, -1, 0, -1693456, -847656704] [2] 98304  
11760.p3 11760bq8 [0, -1, 0, -86256, -18278784] [2] 98304  

Rank

sage: E.rank()
 

The elliptic curves in class 11760bq have rank \(1\).

Modular form 11760.2.a.p

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{9} + 4q^{11} + 2q^{13} + q^{15} - 2q^{17} + 4q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 2 & 2 \\ 8 & 4 & 2 & 8 & 4 & 1 & 8 & 8 \\ 16 & 8 & 4 & 16 & 2 & 8 & 1 & 4 \\ 16 & 8 & 4 & 16 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.